U.S. patent number 11,428,560 [Application Number 15/765,381] was granted by the patent office on 2022-08-30 for estimating flow rate at a pump.
This patent grant is currently assigned to EQUINOR ENERGY AS. The grantee listed for this patent is STATOIL PETROLEUM AS. Invention is credited to Kjetil Fjalestad, Dinesh Krishnamoorthy.
United States Patent |
11,428,560 |
Fjalestad , et al. |
August 30, 2022 |
Estimating flow rate at a pump
Abstract
A method for determining an estimated flow rate of fluid flow in
a pump comprises: obtaining measurements of the pressure and
temperature of fluid at the intake to the pump, the pressure and
temperature of the fluid at the discharge from the pump, and the
electrical power supplied to the pump; determining values
representing either the density of the fluid and the specific heat
capacity of the fluid, or the specific fluid enthalpy based on
measurements and/or historical data; and calculating an estimated
efficiency of the pump and an estimated flow rate of the fluid
based on the measured electrical power, the measured temperatures,
the measured pressures, the determined value for density and the
determined value for specific heat capacity or the determined value
for specific fluid enthalpy.
Inventors: |
Fjalestad; Kjetil (Skien,
NO), Krishnamoorthy; Dinesh (Porsgrunn,
NO) |
Applicant: |
Name |
City |
State |
Country |
Type |
STATOIL PETROLEUM AS |
Stavanger |
N/A |
NO |
|
|
Assignee: |
EQUINOR ENERGY AS (Stavanger,
NO)
|
Family
ID: |
1000006532210 |
Appl.
No.: |
15/765,381 |
Filed: |
October 5, 2016 |
PCT
Filed: |
October 05, 2016 |
PCT No.: |
PCT/NO2016/050200 |
371(c)(1),(2),(4) Date: |
April 02, 2018 |
PCT
Pub. No.: |
WO2017/061873 |
PCT
Pub. Date: |
April 13, 2017 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20180252566 A1 |
Sep 6, 2018 |
|
Foreign Application Priority Data
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01F
15/02 (20130101); G01F 1/88 (20130101); G01F
1/86 (20130101); F04D 13/10 (20130101); G01F
1/34 (20130101); G01F 1/74 (20130101); F04D
15/0088 (20130101); G01F 25/10 (20220101); F05B
2270/301 (20130101); F05B 2270/20 (20130101); F05B
2270/303 (20130101) |
Current International
Class: |
F04D
13/10 (20060101); G01F 1/34 (20060101); G01F
1/86 (20060101); G01F 15/02 (20060101); G01F
25/10 (20220101); G01F 1/74 (20060101); G01F
1/88 (20060101); F04D 15/00 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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|
|
|
|
104632643 |
|
May 2015 |
|
CN |
|
10-2011-0138819 |
|
Dec 2011 |
|
KR |
|
2005/035943 |
|
Apr 2005 |
|
WO |
|
Other References
AE Cattaert, High Pressure Pump Efficiency Determination from
Temperature and Pressure Measurements,IEEE PES PowerAfrica 2007
Conference and Exposition Johannesburg, South Africa, Jul. 16-20,
2007 (Year: 2007). cited by examiner .
Brenne, Lars; Bjorge, Tor; Gilarranz, Jose L.; Koch, Jay M.;
Miller, Harry F. (2005). Performance Evaluation Of A Centrifugal
Compressor Operating Under Wet Gas Conditions.. Texas A&M
University. Turbomachinery Laboratories. (Year: 2005). cited by
examiner .
Search Report dated Feb. 7, 2020 in corresponding Norwegian Patent
Application No. 20180572 with English-language translation. cited
by applicant .
International Search Report and Written Opinion of the
International Searching Authority dated Dec. 14, 2016 in
International (PCT) Application No. PCT/NO2016/050200. cited by
applicant .
Search Report dated Mar. 31, 2016 in corresponding GB Application
No. GB1517537.5. cited by applicant .
Norwegian Search Report dated Oct. 15, 2020 in corresponding
Norwegian Patent Application No. 20180572. cited by applicant .
Russian Search Report dated Feb. 10, 2020 in corresponding Russian
Patent Application No. 2018116575/28(025811). cited by
applicant.
|
Primary Examiner: Marini; Matthew G
Attorney, Agent or Firm: Wenderoth, Lind & Ponack,
L.L.P.
Claims
The invention claimed is:
1. A method for determining an estimated mass flow rate of
multiphase fluids in the oil and gas industry in a pump system
including a pump, the method comprising: obtaining measurements of
a pressure and a temperature of a multiphase fluid at an intake to
the pump, a pressure and a temperature of the multiphase fluid at a
discharge from the pump, and power supplied to the pump system;
determining values representing a specific fluid enthalpy based on
measurements and fluid models and/or historical data; calculating
an estimated efficiency of the pump and an estimated mass flow rate
of the multiphase fluid based on the supplied power, the measured
temperatures, the measured pressures, and the determined value for
specific fluid enthalpy; at least one of using pump specific
efficiency vs mass flow rate curves plotted for varying viscosities
of multiphase fluids, determined using calibration data for the
pump, to determine a viscosity for the multiphase fluid by
determining a viscosity curve with which the estimated flow rate
and the estimated pump efficiency correspond, using pump power vs
mass flow rate curves plotted for varying viscosities of multiphase
fluids, determined using calibration data for the pump, to
determine a viscosity for the multiphase fluid by determining a
viscosity curve with which the estimated flow rate and the
estimated pump power correspond, and obtaining a differential
pressure of the pump, and using pump specific differential pressure
vs mass flow rate curves plotted for varying viscosities of
multiphase fluids, determined using calibration data for the pump,
to determine a viscosity for the multiphase fluid by determining a
viscosity curve with which the estimated flow rate and the
estimated pump differential pressure correspond; and comparing the
calculated estimated efficiency of the pump to a manufacturer's
prescribed efficiency values of the pump, and when the calculated
estimated efficiency of the pump is outside of the manufacturer's
prescribed efficiency values, issuing an alert which indicates at
least one of an error in measured input data, wear on the pump,
damage to the pump, or failure of the pump.
2. The method as claimed in claim 1, wherein the multiphase fluid
passing through the pump is sampled or collected downstream of the
pump, with measurements being taken to determine values for the
specific enthalpy.
3. The method as claimed in claim 1, wherein estimated values for
the specific fluid enthalpy are used, with the estimated values
being derived from fluid property models and from the pressures and
temperatures that are measured at the pump intake and
discharge.
4. The method as claimed in claim 1, further comprising modifying a
pump device in order that it includes temperature and pressure
sensors for the intake and the discharge.
5. The method as claimed in claim 1, further comprising determining
if a stable flow condition exists before using measured temperature
and pressure values in the calculating of the estimated efficiency
and mass flow rate.
6. The method as claimed in claim 1, further comprising allowing a
predetermined time period to elapse after the system is initiated
or after an unstable flow condition is known to be present or has
been detected.
7. The method as claimed in claim 6, further comprising allowing a
predetermined time period to elapse after a change is made to a
control of the pump or to other flow control devices affecting the
flow at the pump.
8. The method as claimed in claim 6, wherein the predetermined time
period is at least 5 minutes.
9. The method as claimed in claim 1, further comprising checking
for changes above a certain threshold in one or more of the
measured pressures, the measured temperatures, the power supplied
to the pump, or the calculated pump efficiency during a
predetermined time period before using measured temperature and
pressure values in the calculating of the estimated efficiency and
mass flow rate.
10. The method as claimed in claim 1, further comprising comparing
the discharge and intake temperatures and checking that the
discharge temperature is higher than or at least the same as the
intake temperature.
11. The method as claimed in claim 1, wherein the calculating of
the estimated efficiency for the pump and the estimated mass flow
rate is carried out based on an assumption that the power supplied
to the pump is converted to mechanical energy and to heat in the
pumped fluid, and that there is no loss of either mass or heat.
12. The method as claimed in claim 1, wherein mass and energy
balances are used to determine the mass flow rate based on the
measured pressure and temperature values, a known cross-sectional
area for the pump, and the determined values for specific fluid
enthalpy.
13. The method as claimed in claim 1, further comprising using
calibration data for the pump to determine a gas fraction in the
pump for compressible fluids based on the estimated mass flow rate
and the efficiency.
14. The method as claimed in claim 1, wherein the pump is a
centrifugal pump.
15. The method as claimed in claim 1, wherein the pump is an
electrical submersible pump (ESP).
16. A non-transient computer programme product comprising
instructions that, when executed, will configure a data processing
device to carry out the method as claimed in claim 1.
17. A non-transient computer programme product comprising
instructions that, when executed, will configure a data processing
device: to receive measurements of pressure and temperature of a
multiphase fluid at an intake to a pump, pressure and temperature
of the multiphase fluid at a discharge from the pump, and
electrical power supplied to the pump; to receive or to determine
values representing a specific fluid enthalpy, based on
measurements and/or historical data; to calculate an estimated
efficiency for the pump and an estimated mass flow rate of the
multiphase fluid based on the measured electrical power, the
measured temperatures the measured pressures, a known
cross-sectional area, and the value for specific fluid enthalpy; at
least one of to use pump specific efficiency vs mass flow rate
curves plotted for varying viscosities of multiphase fluids,
determined using calibration data for the pump to determine a
viscosity for the multiphase fluid by determining a viscosity curve
with which the estimated flow rate and the estimated pump
efficiency correspond, to use pump power vs mass flow rate curves
plotted for varying viscosities of multiphase fluids, determined
using calibration data for the pump, to determine a viscosity for
the multiphase fluid by determining a viscosity curve with which
the estimated flow rate and the estimated pump power correspond,
and to obtain a differential pressure of the pump, and to use pump
specific differential pressure vs mass flow rate curves plotted for
varying viscosities of multiphase fluids, determined using
calibration data for the pump, to determine a viscosity for the
multiphase fluid by determining a viscosity curve with which the
estimated flow rate and the estimated pump differential pressure
correspond; and to compare the calculated estimated efficiency of
the pump to a manufacturer's prescribed efficiency values of the
pump, and when the calculated estimated efficiency of the pump is
outside of the manufacturer's prescribed efficiency values, to
issue an alert which indicates at least one of an error in measured
input data, wear on the pump, damage to the pump, or failure of the
pump.
18. An apparatus for estimating flow rate of multiphase fluids in
the oil and gas industry at a pump, the apparatus comprising a data
processing device arranged: to receive measurements of pressure and
temperature of a multiphase fluid at an intake to a pump, pressure
and temperature of the multiphase fluid at a discharge from the
pump, and electrical power supplied to the pump; to receive or to
determine values representing a specific fluid enthalpy based on
measurements and/or historical data; to calculate an estimated
efficiency for the pump and an estimated mass flow rate of the
multiphase fluid based on the measured electrical power, the
measured temperatures the measured pressures, a known
cross-sectional area, and the value for specific fluid enthalpy; at
least one of to use pump specific efficiency vs mass flow rate
curves plotted for varying viscosities of multiphase fluids,
determined using calibration data for the pump to determine a
viscosity for the multiphase fluid by determining a viscosity curve
with which the estimated flow rate and the estimated pump
efficiency correspond, to use pump power vs mass flow rate curves
plotted for varying viscosities of multiphase fluids, determined
using calibration data for the pump, to determine a viscosity for
the multiphase fluid by determining a viscosity curve with which
the estimated flow rate and the estimated pump power correspond,
and to obtain a differential pressure of the pump, and to use pump
specific differential pressure vs mass flow rate curves plotted for
varying viscosities of multiphase fluids, determined using
calibration data for the pump, to determine a viscosity for the
multiphase fluid by determining a viscosity curve with which the
estimated flow rate and the estimated pump differential pressure
correspond; and to compare the calculated estimated efficiency of
the pump to a manufacturer's prescribed efficiency values of the
pump, and when the calculated estimated efficiency of the pump is
outside of the manufacturer's prescribed efficiency values, to
issue an alert which indicates at least one of an error in measured
input data, wear on the pump, damage to the pump, or failure of the
pump.
19. The apparatus as claimed in claim 18, wherein the data
processing device is arranged to carry out a method for determining
an estimated mass flow rate of the multiphase fluid in a pump
system including the pump, the method comprising: obtaining
measurements of the pressure and temperature of the multiphase
fluid at the intake to the pump, the pressure and temperature of
the multiphase fluid at the discharge from the pump, and the power
supplied to the pump system; determining values representing the
specific fluid enthalpy based on measurements and fluid models
and/or historical data; and calculating the estimated efficiency of
the pump and the estimated mass flow rate of the multiphase fluid
based on the supplied power, the measured temperatures, the
measured pressures, and the determined value for specific fluid
enthalpy.
Description
The invention relates to a method and an apparatus for estimating
the flow rate of fluid flow in a pump, such as a centrifugal pump
for multi-phase flows such as oil and gas flows. The invention may
be used to assess flow rate for various fluids, advantageously
including fluids with varying viscosity or fluid components/phase
fractions.
It is beneficial to be able to determine the flow rate of fluids in
any fluid processing and/or transportation system. For example, in
the oil industry it is important to measure the flow rates of
fluids produced by oil and gas wells. Various pumps are used in
conveying fluids for fluid processing and/or transportation systems
such as oil well systems, and the flow rates through the various
pumps can be important to know, but hard to determine especially
when there is a multiphase fluid, and compressible fluid phase
fractions, and/or a fluid with one or more properties that are hard
to determine.
There are various examples in the prior art relating to determining
flow rates based on pump parameters and making use of the ability
to measure the electrical power supplied to the pump in order to
derive information relating to the pump operating conditions, even
when the pump is in a remote and inaccessible location. For
example, US 2013/317762 discloses a method of determining flow
rates for a well equipped with an electric submersible pump (ESP).
Electrical power is applied to an ESP and controlled with surface
switchgear. A processor receives intake and discharge pressures
from either a single gauge or two gauges installed in the well. The
processor receives a voltage and a current. The processor further
receives at least one static value. The processor calculates an
efficiency to flow rate ratio by applying the received voltage and
current to a power equilibrium equation. The processor obtains a
non-dimensional flow rate by applying the calculated efficiency to
flow rate ratio to the static data. The processor calculates the
flow rate from the non-dimensional flow rate. The processor creates
a log of calculated flow rates.
US 2015/211906 discloses another method for detecting the flow rate
of a centrifugal pump such as an ESP. The method involves
determining the rotation speed of the pump or of the motor driving
the pump, a hydraulic variable of the pump, typically the delivery
pressure and an electrical variable of the drive motor, for example
the electrical power. The flow rate is evaluated by way of these
variables. For this, variables dependent on the flow rate are
determined by way of a mathematical linking of terms of equations
describing physical relations of the pump and drive motor, wherein
one term contains the rotation speed of the pump and a hydraulic
variable of the pump and another term contains an electrical or
mechanical variable of the drive motor of the pump and the rotation
speed of the pump. The flow rate is determined by way of the
functional relation between the flow rate and the dependent
variable.
Such techniques are often referenced as `soft sensors` for the flow
rate. They provide an estimate of the flow rate rather than a
measurement as such. Other technologies used for similar flow rate
measurements include multiphase flow meters (MPFMs). However, there
is still a need for improved techniques for the estimation of flow
rate for pumps such as ESPs and for other pumps, especially for the
pumping of multiphase fluids and compressible fluids. Currently
available wellhead instruments such as MPFMs are expensive and
require extensive calibration, and currently do not provide
acceptable accuracy for viscous flows such as heavy oils. The
existing ESP `soft sensors` also require extensive calibration and
are strongly dependent on fluid viscosity. In addition, repeated
calibration is required over time as the pump is used and its
operating characteristics change due to wear and tear. Variations
in fluid viscosity generate particular challenges in multiphase
fluids such as oilfield production fluids since the viscosity can
vary considerably within a short time period and it cannot easily
be modelled or measured in real-time. The prior art hence has
significant difficulties in dealing with varying viscosity.
Viewed from a first aspect the present invention provides a method
for determining an estimated flow rate of fluid flow in a pump, the
method comprising: obtaining measurements of the pressure and
temperature of fluid at the intake to the pump, the pressure and
temperature of the fluid at the discharge from the pump, and the
electrical power supplied to the pump; determining values
representing either the density of the fluid and the specific heat
capacity of the fluid, and/or the specific fluid enthalpy based on
measurements and/or historical data; and calculating an estimated
efficiency of the pump and an estimated flow rate of the fluid
based on the measured electrical power, the measured temperatures,
the measured pressures, the determined value for density and the
determined value for specific heat capacity or the determined value
for specific fluid enthalpy.
In contrast to known methods a measurement of temperature at both
intake and discharge is included in combination with determination
of density and specific heat capacity, or of the specific fluid
enthalpy. The result of this is that it is possible to determine
the flow rate even when the fluid is a viscous fluid and/or when
the viscosity varies. The method makes use of values for either
density and specific heat capacity together, or just specific fluid
enthalpy, or all of density, specific heat capacity and specific
fluid enthalpy. Where specific fluid enthalpy is known or can be
determined then the method above can also be used when the fluid is
compressible. In addition, where the pump has a known
cross-sectional area at inlet and discharge then even if specific
fluid enthalpy values are not available or not used, so that
density and specific heat capacity must be used instead, then the
method can be used when the fluid is compressible, with the
cross-sectional area being taken into account during the
calculation of pump efficiency and estimated flow rate. Thus it
enables accurate estimation of flow rate through the pump even in
the case of multiphase fluids with varying viscosity, such as
production fluids from an oil and gas well including water as well
as even heavy oils. The prior art does not have this capability.
The proposed method can be used with any pump where the required
pressure and temperature measurements can be obtained, and where
the power supplied to the pump can be determined. There is no
requirement for extensive calibration, even when the pump
performance changes due to wear of the pump. However, if
calibration is available then advantageously the method can be
extended to also make use of the calibration data and to determine
the fluid viscosity, providing a further advantage compared to the
prior art ESP systems mentioned above.
The invention is, in part, based on a realisation that although the
viscosity cannot be measured or assigned an accurate estimated
value, it is possible to determine suitably accurate values for the
density and the specific heat capacity of the fluid and/or for the
specific fluid enthalpy. In most typical scenarios these parameters
are constant over relatively long periods of time, unlike the
density which varies quickly and unpredictably. There is hence no
requirement for an instantaneous measure of density, specific heat
capacity, or fluid enthalpy. Instead a measurement can be obtained
over a longer period of time, for example by using a slower
measurement technique, or a measurement can be taken of fluids that
have already passed through the pump, with this `historical`
measurement being used to give a suitable value for density and for
specific heat capacity. Thus, in some example implementations the
fluid passing through the pump can be periodically sampled or
collected downstream of the pump, with measurements being taken
using known techniques, and these measurements can be used in the
present method as suitably accurate values for density and specific
heat capacity and/or specific fluid enthalpy. Such periodic
measurements may for example be taken hourly, daily, weekly, or
monthly depending on the particular situation. Alternatively,
estimated values for fluid density, specific heat capacity and/or
specific fluid enthalpy can be used. These may be derived from
fluid property models and from the pressures and temperatures that
are measured at the pump intake and discharge.
The measured temperatures and pressures may be obtained from
conventional sensors in place at the inlet and discharge of the
pump. It is already known in the art to use such sensors for
monitoring purposes and for process control. The method may include
providing temperature and pressure sensors if necessary. In
particular, the method may include providing a sensor for the
discharge temperature in the case where an existing pump has inlet
and discharge pressure sensors, and an inlet temperature sensor,
which is a typical arrangement. It is an advantage of the invention
that often only this single additional temperature sensor will be
required to adapt an existing pump for use with the method, or
indeed in some cases there may be no additional sensors needed.
Another advantage is that the method can be used in the case of a
submersible pump (ESP) where the motor is also inside the well pipe
regardless of the location of the temperature sensor at the intake
sensor relative to the motor. This, the sensor may be upstream or
downstream the motor. If the sensor is downstream of the motor then
the motor efficiency should be included when calculating the power
supplied to the pump.
In order for the method to be most accurate it is preferred to
avoid measurements taken during periods of transition or unstable
flow, for example after significant changes are made to the control
of the pump and/or to other flow control devices upstream or
downstream of the pump that affect the flow conditions at the pump.
Such other flow control devices might include valves, pumps and so
on. Transition or unstable flow can also result from outside
sources, such as changes in downhole in an oil and gas installation
resulting from natural variations or geological formations. The
method therefore may include a step of determining if a stable flow
condition exists, for example by allowing a predetermined time
period to elapse after the system is initiated or after an unstable
flow condition is known to be present or has been detected. In some
examples this may include allowing a predetermined time period to
elapse after a change is made to the control of the pump or to
other flow control devices affecting the flow at the pump. The
predetermined time period may be 5 minutes or 10 minutes, for
example. Alternatively or in addition, the method may include
checking for changes above a certain threshold in one or more of
the measured pressures, the measured temperatures, the power
supplied to the pump system or the calculated pump efficiency
during that time period. If there is a change in excess of the
threshold then it is deemed that flow is unstable, and hence more
time is allowed to elapse to check for a stable condition.
Typically the threshold would be for changes higher than 1-5% of
the measured difference (e.g. the variation should be less than
.+-.0.1.degree. C. if the temperature increase from intake to
discharge is 2.degree. C.) although the threshold will be system
dependent. For some cases a dynamic model (differential equations)
could compensate for the transients and an observer (e.g. a Kalman
filter) could be applied to provide valid flow rate estimated even
during transient periods.
Preferably, the method further includes comparing the estimated
efficiency of the pump to the manufacturer's efficiency values.
This provides a check to ensure that there are no faults in the
system and that there are no outside influences resulting in the
method becoming inaccurate or ineffective. For example, a sensor
fault due to physical (e.g. clogging) or electrical problems can
result in a bad reading, which would not provide accurate results.
An unstable flow condition, such as unstable flow as discussed
above, will also give inaccurate estimation of the flow rate. There
could also be an unexpected and quick change in density or specific
heat capacity if the fluid composition changes suddenly, for
example due to unexpected large increase in water cut in an oil and
gas production fluid. Comparing the calculated efficiency from the
current method against the expected efficiency for the pump
provides a means of checking the input data and hence identifying
any potential bad values.
Additional checks may also be included. For example, the discharge
and intake temperatures may be compared to check that the discharge
temperature is higher than or at least the same as the intake
temperature. A discharge temperature that is lower than the intake
temperature would tend to indicate zero flow or reverse flow, or
some other problem.
The cross-sectional area of the pump will of course typically be a
known quantity based on the pump specification. In general the
cross-sectional area of the inlet and the discharge will be
identical.
The electrical power supplied to the pump may be measured in any
suitable way. This electrical power may be power supplied directly
to the pump to a motor that is integral to the pump, or electrical
power supplied to a motor outside of the pump, where this motor
powers the pump via a mechanical coupling. In some example
embodiments the method involves measurement of current and voltage
supplied to the pump (which may be supplied either directly or via
a separate motor). Advantageously, this can be done remotely from
the pump, with an adjustment being made to take account of losses
in the conductors between the measurement point and the pump
motor.
The step of calculating an estimated flow rate may be carried out
using any suitable formulae relating the measured and estimated
values. One preferred implementation is based on the assumption
that the power supplied to the pump is converted to mechanical
energy and to heat in the pumped fluid, and that there is no loss
of either mass (i.e. no leakage) or of heat (i.e. all the waste
heat is taken by the fluid). This would be applicable to ESPs and
other downhole systems, as well as other systems were the heat leak
is negligible. For where there is a non-negligible heat loss then
the heat loss may be calculated/estimated with this being included
in the calculation. Mass and energy balances may be used to
determine the flow rate based on the measured pressure and
temperature values, the known cross-sectional area for the pump,
and the determined values for density and specific heat capacity or
specific fluid enthalpy. Suitable mass and energy balances are set
out below by way of example as equations (1) and (2). The method
may make use of these equations, or mathematical equivalents
thereof.
It will be appreciated that various models may be used to determine
a mass flow rate for the fluid based on the input parameters used
for the present method. One example is set out in equations (3) to
(9) below, making use of density and specific heat capacity.
Another possibility is to use fluid enthalpy, as show in equations
(44 to 47). The method may make use of these equations and further
may include one or more of equations (12) to (32), or combinations
thereof as appropriate in order to obtain one or more of the mass
flow rate, volume flow rate or pump efficiency. Mathematical
equivalents of these equations may also be used. The method may
include alternative solutions for use with incompressible fluids
(or fluids that can be approximated as incompressible) and for
compressible fluids. In the case of compressible fluids then a
non-linear method may be used to solve the equations.
Optionally, the method may include using calibration data for the
pump to determine a viscosity for the mixed fluid based on the
estimated flow rate and on the estimated pump efficiency. Where a
viscous fluid is present then this step may include the use of
viscosity correction factors, for example as defined in equations
(33) to (38) below. Additionally, when a compressible fluid is
present, then the method may include the use of gas correction
factor functions to estimate the gas volume fraction or the gas
mass fraction inside the pump for example as defined in equations
(39) to (43).
The pump may be a centrifugal pump. The approach described above
has been found to provide accurate results for this type of pump.
The pump may for example be an electrical submersible pump
(ESP).
Preferably the method is used to estimate flow rates for multiphase
fluids, for example in the oil and gas industry. Thus, the pump may
be a pump in an oil and gas installation. The fluid may be a
multiphase production fluid from an oil well, such as a mixture of
oil, water and/or gas. The method has been found to provide
particular advantages over prior art methods when the fluid
includes viscous components such as heavy oils. Thus, in some
examples the fluid includes heavy oils.
In a further aspect the invention provides a computer programme
product comprising instructions that, when executed, will configure
a data processing device to carry out the method described above in
the first aspect and the preferred/optional features thereof. Thus,
there may be a computer programme product comprising instructions
that, when executed, will configure a data processing device to
receive measurements of pressure and temperature of fluid at an
intake to a pump, pressure and temperature of the fluid at a
discharge from the pump, and electrical power supplied to the pump;
to receive or to determine values representing the density of the
fluid and the specific heat capacity of the fluid, and/or the
specific fluid enthalpy, based on measurements and/or historical
data; and to calculate an estimated efficiency for the pump and an
estimated flow rate of the fluid based on the measured electrical
power, the measured temperatures the measured pressures, the known
cross-sectional area, the value for density and the value for
specific heat capacity or the value for specific fluid
enthalpy.
The computer programme product may include an algorithm that is
intended to run in various environments such as a process control
system, on a dedicated computer system, or in combination with
other production related software.
The invention further provides an apparatus for estimating flow
rate of fluid at a pump, the apparatus comprising a data processing
device arranged to receive measurements of pressure and temperature
of fluid at an intake to a pump, pressure and temperature of the
fluid at a discharge from the pump, and electrical power supplied
to the pump; to receive or to determine values representing the
density of the fluid and the specific heat capacity of the fluid
and/or the specific fluid enthalpy based on measurements and/or
historical data; and to calculate an estimated efficiency for the
pump and an estimated flow rate of the fluid based on the measured
electrical power, the measured temperatures the measured pressures,
the known cross-sectional area, the value for density and the value
for specific heat capacity or the value for specific fluid
enthalpy. The data processing device may be arranged to carry out
any or all of the method steps described above.
The apparatus may be a control apparatus for the pump and/or for an
installation including the pump. For example the apparatus may be a
control apparatus for an oil and gas installation and the pump may
be for pumping fluids from the oil and gas installation, such as
multiphase fluids. The apparatus may include the pump, which may be
a centrifugal pump. The pump may be an ESP.
BRIEF DESCRIPTION OF THE DRAWINGS
Certain preferred embodiments of the invention will now be
described by way of example only and with reference to the
accompanying drawings in which:
FIG. 1 shows an ESP with motor and pump inside the well;
FIG. 2 is a plot showing measured flow rate from an ESP test--solid
line--and the flow rate estimated with the model in equation
(15)--dashed line;
FIG. 3 is a plot showing measured efficiency from the ESP
test--solid line--and efficiency estimated with the model in
equation (16)--dashed line;
FIG. 4 shows the recorded temperature increase from the ESP
test--solid line--and the same values estimated with the model in
equation (15)--dashed line--when the measured flow rate was used as
an input for the mode;
FIG. 5 shows a plot of flow rate from a flow loop for an ESP
test--blue line--and the flow rate estimated with the model in
equation (23)--red line;
FIG. 6 is a plot of efficiency from the flow loop--solid line--and
the efficiency estimated with equation (26)--dashed line and
equation (27)--bold line:
FIG. 7 shows, in the top plot, the flow rate obtained from a flow
loop for an ESP test--solid line--and the flow rate estimated with
the multiphase model as shown in equation (23)--dashed line, and,
in the bottom plot, the gas volume fraction;
FIG. 8 shows viscosity obtained from the flow loop--solid line--and
viscosity estimated with the multiphase model--dashed line; and
FIG. 9 is an example of ESP efficiency curves for various fluid
viscosities.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
The estimation of flow rate through a pump will be described below
with reference to an Electrical Submersible Pump (ESP) as an
example. The ESP is a centrifugal pump which is installed inside
the well with the electrical motor as shown in FIG. 1. The motor
and the pump convert electric power to heat and mechanical energy
for the pumped fluid. The example calculations relate firstly to an
incompressible fluid, for example an oil and water mixture, and
secondly to a compressible fluid, for example an oil, water and gas
mixture.
The pump supplied power, P.sub.Pump, will be converted to
mechanical energy, P.sub.Fluid, or heat, Q.sub.Fluid, in the pumped
fluid. It is assumed that the fluid mass inside the pump is
constant, and there is no loss of either mass (no leak out of the
well) or heat from the system (fluid is heated). .zeta. is specific
enthalpy. Applying mass and energy balances will give:
w=w.sub.In=w.sub.Out.apprxeq.q.sub.In.beta..sub.MixIn.apprxeq.q.sub.Out.b-
eta..sub.MixOut (1)
P.sub.Pump=w(.zeta..sub.Out.sup.0-.zeta..sub.In.sup.0)+.DELTA.Q.sub.Loss=-
.DELTA.P.sub.Fluid,Mecanical+.DELTA.Q.sub.Fluid,Heat+.DELTA.Q.sub.Loss
(2)
The stagnation enthalpy, .zeta..sup.0, and the specific enthalpy,
.zeta., as expressed as set out below.
.zeta..sup.0=.zeta.+1/2v.sup.2+gh .zeta.=u+pv
where v is the fluid velocity, g is specific gravitation, h is the
height, u is internal energy, and p is pressure.
For downhole pumps both the motor and the pump is placed in the
flowing pipe, thus the heat loss from the pumping system can be
neglected since this heat is transferred to the fluid and the
temperature on the discharge is measured. Then equation (2) can be
written:
P.sub.Pump=W(.zeta..sub.Out-.zeta..sub.In)=.DELTA.P.sub.Fluid,Mechanical+-
.DELTA.Q.sub.Fluid,Heat (2a)
Based on the equations (1) and (2a) the mass flow rate can be
determined using specific fluid enthalpy obtain by estimation or
measurement of the fluid in accordance with equations (44) to (47)
below. Alternatively, using density and specific heat capacity then
following model may be derived to determine the mass flow rate,
w:
.function..rho..rho.--.times.--.times..times..times..times..times..times.-
--.times..times..times.--.times..times..times..function..times.--.times..t-
imes.--.times..times..times..rho..times..times..function..times..rho..time-
s..rho..times..times..rho..times..times..function..rho..rho.--.times..time-
s.--.times..times..times..rho..times..rho..times. ##EQU00001##
The electric power, P.sub.Pump, to the pump (or the motor) can be
measured or calculated from the voltage and current:
P.sub.Pump=.PHI.U.sub.MotorI.sub.Motor=.PHI.(U.sub.Motor-R.sub.CableI.sub-
.Motor) (10) .PHI.=PF {square root over (3)}={right arrow over (3)}
sin(Q.sub.U.angle.1) (11)
If the pumped fluid is incompressible, the fluid density at the
intake and the discharge will be equal. If it is assumed that the
flowing areas are equal as well, the equation can be simplified
as:
.function..rho.--.times..times.--.times..times. ##EQU00002## If the
specific heat capacity is the same at the inlet and outlet as well,
the equation can be expressed:
.function..rho..function. ##EQU00003##
Now the mass flow rate, w, or the volume flow rate, q, can be
determined:
.rho..times..times..times..rho..function..eta..rho..times..times..times..-
rho..function..eta..times..times. ##EQU00004##
FIG. 2 shows the results of an example calculation using equation
(15). A Centrilift.TM. ESP was tested with all relevant input and
output parameters being measured, and the flow rates also being
measured. The specific heat capacity was c.sub.P=1800, and the
remaining variables were measured in the flow loop of the test rig.
FIG. 2 illustrates the measured flow rate as compared to the flow
rate estimated using equation (15). It will be appreciated that
there is a close correspondence between the two flow rates,
especially during steady state/stable flow conditions.
The pump efficiency, .eta., may be expressed as the pump power
turned into mechanical fluid energy:
.eta..function..rho..times..times..function. ##EQU00005##
FIG. 3 shows the results of an example calculation using equation
(16). The same Centrilift.TM. ESP test was used as for FIG. 2. FIG.
3 illustrates the measured efficiency as compared to the efficiency
estimated using equation (16). It will be appreciated that there is
a close correspondence between the two efficiency values,
especially during steady state/stable flow conditions.
Alternatively, from the fluid temperature increase:
.eta..function. ##EQU00006##
Combining the equations (16) and (17) enables direct calculation of
the pump efficiency independent of the applied break horse power,
P.sub.Pump via equation (18) The pump efficiency should be verified
to be in the pump range (as specified by the manufacturer) and only
valid if T.sub.Out>T.sub.In+.DELTA.T.sub.min and
p.sub.Out>P.sub.In+.DELTA.p.sub.Min before applied for flow rate
estimation according to equation (14) or (15). If the pump
efficiency from the calculation is outside of the range from the
manufacturer then an alert is made regarding potentially bad
measurements or some other outside influence leading to bad
results, such as an unstable flow during the measurement
period.
.eta..times..rho..times. ##EQU00007##
Both the estimated flow rate (FIG. 2) pump efficiency (FIG. 3)
deviate from the flow loop measurements. The main uncertainty of
the input data is the measured temperature change. To evaluate this
input variable, the model has been used to calculate the
temperature increase and compare with the flow loop measurement.
The measured and estimated temperature changes (to achieve the flow
loop measured flow rate) are shown in FIG. 4.
If the pumped fluid is compressible, the calculations are more
complex as indicated in equation (19). Since this model is a
3.sup.rd order equation, a non-linear method (e.g. Newton Raphson)
may be used to solve the equation. If we assume that the cross
sectional areas at intake and discharge are equal, the equation can
be written:
.function..rho..rho.--.times..times.--.times..times..times..times..rho..r-
ho. ##EQU00008##
The next assumptions are that the phase mass fractions, x.sub.i,
and fluid (phase) properties are known and that there is no slip
between the phases. The following relations for mixed heat capacity
and density may be established:
--.times..times..times..function.--.times..function..rho..times..times..f-
unction..rho..function. ##EQU00009##
The flow rate may be formulated as 3.sup.rd order equation:
.times..times..rho..rho..times..rho..rho.--.times..times.--.times..times.-
.times..rho..rho..times..function..rho..rho.--.times.--.times..function..r-
ho..rho. ##EQU00010##
The efficiency of the pump may be expressed as the fraction of the
applied power that is transformed into mechanical energy, similar
to equation (16), but the fluid compressibility should be accounted
for:
.times..times..eta..function..rho..rho..times..times..rho..rho..times..fu-
nction..eta..function.--.times..times.--.times..times..eta..eta.--.times..-
times.--.times..times..times..rho..rho..function..eta..times..function.--.-
times..times.--.times..times..times..rho..rho. ##EQU00011##
Equation (26) can be reformulated in the efficiency, .eta., as a
3.sup.rd order formula:
.times..eta..times..eta..times..eta..times..function.--.times..times.--.t-
imes..times..times..rho..rho..times..rho..rho..times..times..function.--.t-
imes..times.--.times..times..times..rho..rho. ##EQU00012##
The models in equations (23) and (27) are non-linear and the
solution may be found using the Newton-Raphson method. Then the
derivate of the function will be used:
f.sub.w.sup.1(w)=3w.sup.2+c.sub.1(A,.rho..sub.MixIn,.rho..sub.MixOut,c.su-
b.P . . . MixIn,c.sub.P . . .
MixOut,p.sub.In,p.sub.Out,T.sub.In,T.sub.Out) (30)
f.sub..eta..sup.1(.eta.)=3.eta..sup.2-6.eta.+(3+b.sub.1+b.sub.2)
(31)
The solution of the variable is now found by iterations on x (which
is w or .eta. in the equations above):
.function..function. ##EQU00013##
FIG. 5 shows an example calculation using equation (23). A
Centrilift.TM. ESP was tested with all relevant input and output
parameters being measured, and the flow rates also being measured.
The specific heat capacity was c.sub.P=1750, and the remaining
variables were measured in the flow loop. FIG. 5 illustrates the
measured flow rate as compared to the flow rate estimated using
equation (23). It will be appreciated that there is a close
correspondence between the two flow rates, especially during steady
state/stable flow conditions.
FIG. 6 shows data from the same test in relation to efficiency. The
measured values for efficiency are plotted along with calculated
values from equations (26) and (27) based on pressure and
temperature differentials respectively.
FIG. 7 illustrates, in the top plot, a comparison of flow rates
from the flow loop for an ESP test and flow rates calculated using
equation (23), with the bottom plot showing the gas volume fraction
(GVF). It will be appreciated that the large variations in GVF
result in substantial variations in compressibility of the fluid
through the pump. Nonetheless, the estimated flow rates from
equation (23) follow the measured values closely.
The pump curves and the viscosity correction factors may be used to
find the fluid viscosity as shown in equation (38).
.mu..mu..function..mu..function..times..times..rho..rho..eta..function..e-
ta..eta..eta..eta..mu..function..eta. ##EQU00014##
While the absolute difference between the estimated viscosity and
the estimated viscosity at the previous iteration is greater than a
defined tolerance .epsilon., iterate on equations (33)--(38) to
estimate the viscosity. Equation (33) saves the viscosity estimated
at the previous step to be compared with the estimated viscosity of
the current step. Initially, this can be set to an initial guess
value defined by the user. Viscosity correction factor for flow is
computed for this viscosity (34) The estimated flow rate
w.sub.Estimate from (14) is converted to reference base case
(water, 60 Hz) using viscosity correction factor and affinity laws
(35). The base efficiency .eta..sub.base is then computed from the
reference base curve implemented in the form of a lookup table
(36). Using the base efficiency and the estimated efficiency
.eta..sub.Estimate from (16), (17) or (18), the viscosity
correction factor for efficiency is computed (37). The viscosity is
then estimated from the VCF function for efficiency (38). This is
then iterated until the change in the viscosity is less than a
defined tolerance value. FIG. 8 shows the viscosity as measured
from the flow loop for the ESP test compared against the calculated
viscosity using the model described above.
It is also possible to determine the fluid viscosity from
efficiency, flow rate, mass flow rate, pump frequency, and pump
specific calibration data/efficiency curves if this is available.
An example of such curves is shown in FIG. 9. When the flow rate
and efficiency is known then viscosity can be read from the graph.
As well as this, other pump specific relationships like Dp vs flow,
or power vs flow may be used.
For Multiphase flow through the ESP, the GVF can be estimated using
the Gas correction factor GCF and the estimated efficiency from
(16), (17) or (18). When gas enters the ESP, the performance of the
pump is affected and this can be observed in the differential
pressure and the brake horsepower (BHP) of the pump. To account for
the effect to gas in the system, the co-called Gas correction
factors are modelled for dp and BHP. The GCF for dp and BHP are
primarily a function of the gas fraction or the GVF and are
modelled using experimental data. Estimation of the GVF using the
GCF can be done using the equations below.
.function..mu..function..times..times..rho..rho..eta..function..eta..eta.-
.eta..eta..function..eta. ##EQU00015##
As noted above, specific fluid enthalpy values can be determined as
an alternative to using density and specific heat capacity. In this
case, starting with equations (1) and (2a) above, then the
equations below can be used to find the efficiency and hence the
flow rate. The fluid enthalpy can be found from fluid data bases,
and thus calculated based on the actual pressure and
temperature
.function. .function. .times..times..times. .function.
##EQU00016##
where x.sub.i is the mass fraction of phase no i.
Further the efficiency .eta..sub.i may be found from the enthalpy
directly as:
.eta. .function. .function. .function. .function..DELTA.
.function..DELTA..times..times..DELTA.
.function..DELTA..times..times..DELTA..times..times. ##EQU00017##
The enthalpy function may be defined as a polynomial function in p
and T: .zeta..sub.i=a.sub.0+a.sub.pp+a.sub.TT+a.sub.pTpT+ . . .
+a.sub.MpNTp.sup.MT.sup.n (47)
By way of a summary a review of an example process is set out
below. To ensure robust and accurate flow rate calculations some
precautions are necessary as explained above. First, the input
measurements P.sub.Pump, p.sub.In, T.sub.In, p.sub.Out, T.sub.Out
are obtained. Then these values are checked to ensure that they are
suitable, for example by checking that the last value is in line
with the measurements during a given preceding period (e.g. not
deviate more than a given value from the average value during the
last 5 minutes). This ensures that the measurements are stable. It
is also possible to adjust for dynamic effects by predicting the
measurement(s) based on the input data. An estimator such as a
Kalman filter could be used in this case. If the measurements are
not suitable then in some cases they might be corrected using a
model or the like. Alternatively the process may require a waiting
period of the type discussed above to allow for a steady stable
state to be achieved.
If the measurements are suitable then the appropriate parts of the
above model are utilised to calculate the pump efficiency will be
determined. The calculated efficiency should be verified, and if it
is in line with manufacturer data then it is accepted. If the
efficiency is outside the range, then an alert is made to indicate
that something is wrong either with the:
1. Measured input data (operator should check),
2. Pump (wear, tear, failure) which should be notified, or
3. Applied fluid properties (fluid model update may be
required)
If desired and the pump specific parameters are available then the
fluid viscosity may be directly determined.
In the above analysis since the ESP used as an example has the
motor and the pump submerged in the fluid the heat loss can be
ignored. The proposed technique can be adapted for any pump or
compressor where the applied electric power is measured or can be
determined. The same model can be used to find the flow rate
provided that the heat loss, Q.sub.Loss, is compensated for. This
may be done with a simple model:
Q.sub.Loss.apprxeq.H.sub.A(T.sub.Out-T.sub.Env) (48)
The heat transfer coefficient, H.sub.A, may be adapted or
determined from the equipment size and location. The environment
temperature, T.sub.Env, should also be measured for this
situation.
Thus, it will be appreciated that the proposed estimation of flow
rate provides accurate results, as evidenced by the comparisons in
the Figures, and furthermore that there are various advantages
compared to known systems as in US 2013/317762 and US 2015/211906.
The fluid viscosity is not required to be measured or estimated,
which simplifies the calculations significantly and also allows for
a greater range of fluids to be the basis for the calculations,
including for example heavy oils. The compressibility (i.e. gas
fraction) will not significantly affect the accuracy of the
results, which means that the estimation technique provides
important advantages in relation to multiphase flow, such as
pumping of oil and gas mixtures. In addition, it is not necessary
to test the pump with varying fluid viscosity for calibration
purposes in order to obtain accurate flow rate estimates, although
if suitable calibration data is available then this can
advantageously be used to determine the fluid viscosity.
* * * * *